Remark 2Let R be an Euclidean domain such for every aR
we can choose a canonical associate denoted
by normal(a) and called the normal form of a.
Because of the polynomial case, the unit u such
that
a = unormal(a) is denoted
lc(a) and called the leading coefficient of a.
Then normal(rk) where rk is the result
of Algorithm 1 can be called
THE GCD of a and b.
This leads to the following AXIOM code.